They actually can't. We asked. It's apparently an old enough phone that they don't support doing anything with it anymore. It predates even having mini-USB conenctors on the phone and has LG's proprietary connector from that time period. The Verizon cloud data backup service doesn't support it anymore; going to the mobile web on the phone just produces a message that the mobile data is not supported on this phone anymore.
I finally wound up typing all her contacts into a spreadsheet and generating Vcards for them all, then putting all the Vcards in a text file, transferring the file to the new phone via Bluetooth, and importing all the contacts that way.